Systems and methods for endoscopic angle-resolved low coherence interferometry

ABSTRACT

Fourier domain a/LCI (faLCI) system and method which enables in vivo data acquisition at rapid rates using a single scan. Angle-resolved and depth-resolved spectra information is obtained with one scan. The reference arm can remain fixed with respect to the sample due to only one scan required. A reference signal and a reflected sample signal are cross-correlated and dispersed at a multitude of reflected angles off of the sample, thereby representing reflections from a multitude of points on the sample at the same time in parallel. Information about all depths of the sample at each of the multitude of different points on the sample can be obtained with one scan on the order of approximately 40 milliseconds. From the spatial, cross-correlated reference signal, structural (size) information can also be obtained using techniques that allow size information of scatterers to be obtained from angle-resolved data.

RELATED APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 12/538,309 entitled “SYSTEMS AND METHODS FORENDOSCOPIC ANGLE-RESOLVED LOW COHERENCE INTERFEROMETRY,” filed on Aug.10, 2009, which is herein incorporated by reference in its entirety andwhich is a continuation application of U.S. patent application Ser. No.11,548,648, now U.S. Pat. No. 7,595,889, entitled “SYSTEMS AND METHODSFOR ENDOSCOPIC ANGLE-RESOLVED LOW COHERENCE INTERFEROMETRY,” filed onOct. 11, 2006, which is herein incorporated by reference in itsentirety, which claims priority to U.S. Provisional Patent ApplicationNo. 60/725,603 entitled “SYSTEMS AND METHODS FOR ENDOSCOPICANGLE-RESOLVED LOW COHERENCE INTERFEROMETRY,” filed on Oct. 11, 2005,also incorporated herein by reference in its entirety.

This application is also related to U.S. Pat. No. 7,102,758 entitled“FOURIER DOMAIN LOW-COHERENCE INTERFEROMETRY FOR LIGHT SCATTERINGSPECTROSCOPY APPARATUS AND METHOD,” which is incorporated herein byreference in its entirety.

FIELD

Fourier domain angle-resolved low coherence interferometry (faLCI)system and method that enables data acquisition of angle-resolved anddepth-resolved spectra information of a sample, in which depth and sizeinformation about the sample can be obtained with a single scan at rapidrates for in vivo applications in particular.

BACKGROUND

Examining the structural features of cells is essential for manyclinical and laboratory studies. The most common tool used in theexamination for the study of cells has been the microscope. Althoughmicroscope examination has led to great advances in understanding cellsand their structure, it is inherently limited by the artifacts ofpreparation. The characteristics of the cells can only been seen at onemoment in time with their structure features altered because of theaddition of chemicals. Further, invasion is necessary to obtain the cellsample for examination.

Thus, light scattering spectrography (LSS) was developed to allow for invivo examination applications, including cells. The LSS techniqueexamines variations in the elastic scattering properties of cellorganelles to infer their sizes and other dimensional information. Inorder to measure cellular features in tissues and other cellularstructures, it is necessary to distinguish the singly scattered lightfrom diffuse light, which has been multiply scattered and no longercarries easily accessible information about the scattering objects. Thisdistinction or differentiation can be accomplished in several ways, suchas the application of a polarization grating, by restricting or limitingstudies and analysis to weakly scattering samples, or by using modelingto remove the diffuse component(s).

As an alternative approach for selectively detecting singly scatteredlight from sub-surface sites, low-coherence interferometry (LCI) hasalso been explored as a method of LSS. LCI utilizes a light source withlow temporal coherence, such as broadband white light source forexample. Interference is only achieved when the path length delays ofthe interferometer are matched with the coherence time of the lightsource. The axial resolution of the system is determined by the coherentlength of the light source and is typically in the micrometer rangesuitable for the examination of tissue samples. Experimental resultshave shown that using a broadband light source and its second harmonicallows the recovery of information about elastic scattering using LCI.LCI has used time depth scans by moving the sample with respect to areference arm directing the light source onto the sample to receivescattering information from a particular point on the sample. Thus, scantimes were on the order of 5-30 minutes in order to completely scan thesample.

Angle-resolved LCI (a/LCI) has been developed as a means to obtainsub-surface structural information regarding the size of a cell. Lightis split into a reference and sample beam, wherein the sample beam isprojected onto the sample at different angles to examine the angulardistribution of scattered light. The a/LCI technique combines theability of (LCI) to detect singly scattered light from sub-surface siteswith the capability of light scattering methods to obtain structuralinformation with sub-wavelength precision and accuracy to constructdepth-resolved tomographic images. Structural information is determinedby examining the angular distribution of the back-scattered light usinga single broadband light source is mixed with a reference field with anangle of propagation. The size distribution of the cell is determined bycomparing the osciallary part of the measured angular distributions topredictions of Mie theory. Such a system is described in CellularOrganization and Substructure Measured Using Angle-ResolvedLow-Coherence Inteferometry, Biophysical Journal, 82, April 2002,2256-2265, incorporated herein by reference in its entirety.

The a/LCI technique has been successfully applied to measuring cellularmorphology and to diagnosing intraepithelial neoplasia in an animalmodel of carcinogenesis. The inventors of the present applicationdescribed such a system in Determining nuclear morphology using animproved angle-resolved low coherence interferometry system in OpticsExpress, 2003, 11(25): p. 3473-3484, incorporated herein by reference inits entirety. The a/LCI method of obtaining structural information abouta sample has been successfully applied to measuring cellular morphologyin tissues and in vitro as well as diagnosing intraepithelial neoplasiaand assessing the efficacy of chemopreventive agents in an animal modelof carcinogenesis. a/LCI has been used to prospectively grade tissuesamples without tissue processing, demonstrating the potential of thetechnique as a biomedical diagnostic.

Initial prototype and second generation a/LCI systems required 30 and 5minutes respectively to obtain similar data. These earlier systemsrelied on time domain depth scans just as provided in previous LCI basedsystems. The length of the reference arm of the interferometer had to bemechanically adjusted to achieve serial scanning of the detectedscattering angle. The method of obtaining angular specificity wasachieved by causing the reference beam of the interferometry scheme tocross the detector plane at a variable angle. This general method forobtaining angle-resolved, depth-resolved backscattering distributionswas disclosed in U.S. Pat. No. 6,847,456 entitled “Methods and systemsusing field-based light scattering spectroscopy,” which is incorporatedby reference herein in its entirety.

Other LCI prior systems are disclosed in U.S. Pat. Nos. 6,002,480 and6,501,551, both of which are incorporated by reference herein in theirentireties. U.S. Pat. No. 6,002,480 covers obtaining depth-resolvedspectroscopic distributions and discusses obtaining the size ofscatterers by observing changes in wavelength due to elastic scatteringproperties. U.S. Pat. No. 6,501,551 covers endoscopic application ofinterferometric imaging and does anticipate the use of Fourier domainconcepts to obtain depth resolution. U.S. Pat. No. 6,501,551 does notdiscuss measurement of angularly resolved scattering distributions, theuse of scattered light to determine scatterer size by analysis ofelastic scattering properties, nor the use of an imaging spectrometer torecord data in parallel, whether that data is scattering or imagingdata. Finally, U.S. Pat. No. 7,061,622 discusses fiber optic means formeasuring angular scattering distributions, but does not discuss theFourier domain concept. Also because it describes an imaging technique,the embodiments all include focusing optics which limit the regionprobed.

SUMMARY OF THE DETAILED DESCRIPTION

Embodiments disclosed herein involve a new a/LCI technique calledFourier domain a/LCI (faLCI), which enables data acquisition at rapidrates using a single scan, sufficient to make in vivo applicationsfeasible. The embodiments disclosed herein obtain angle-resolved anddepth-resolved spectra information about a sample, in which depth andsize information about the sample can be obtained with a single scan,and wherein the reference arm can remain fixed with respect to thesample due to only one scan required. A reference signal and a reflectedsample signal are cross-correlated and dispersed at a multitude ofreflected angles off of the sample, thereby representing reflectionsfrom a multitude of points on the sample at the same time in parallel.

Since this angle-resolved, cross-correlated signal is spectrallydispersed, the new data acquisition scheme is significant as it permitsdata to be obtained in less than one second, a threshold determined tobe necessary for acquiring data from in vivo tissues. Information aboutall depths of the sample at each of the multitude of different points onthe sample can be obtained with one scan on the order of approximately40 milliseconds. From the spatial, cross-correlated reference signal,structural (size) information can also be obtained using techniques thatallow size information of scatterers to be obtained from angle-resolveddata.

The faLCI technique of the disclosed embodiments uses the Fourier domainconcept to acquire depth resolved information. Signal-to-noise andcommensurate reductions in data acquisition time are possible byrecording the depth scan in the Fourier (or spectral) domain. The faLCIsystem combines the Fourier domain concept with the use of an imagingspectrograph to spectrally record the angular distribution in parallel.Thereafter, the depth-resolution of the disclosed embodiments isachieved by Fourier transforming the spectrum of two mixed fields withthe angle-resolved measurements obtained by locating the entrance slitof the imaging spectrograph in a Fourier transform plane to the sample.This converts the spectral information into depth-resolved informationand the angular information into a transverse spatial distribution. Thecapabilities of faLCI have been initially demonstrated by extracting thesize of polystyrene beads in a depth-resolved measurement.

Various mathematical techniques and methods are provided for determiningsize information of the sample using the angle-resolved,cross-correlated signal.

The embodiments disclosed herein are not limited to any particulararrangement. In one embodiment, the apparatus is based on a modifiedMach-Zehnder interferometer, wherein broadband light from asuperluminescent diode is split into a reference beam and an input beamto the sample by a beamsplitter. In another embodiment, a unique opticalfiber probe can be used to deliver light and collect the angulardistribution of scattered light from the sample of interest.

The a/LCI method can be a clinically viable method for assessing tissuehealth without the need for tissue extraction via biopsy or subsequenthistopathological evaluation. The a/LCI system can be applied for anumber of purposes: early detection and screening for dysplasticepithelial tissues, disease staging, monitoring of therapeutic actionand guiding the clinician to biopsy sites. The non-invasive,non-ionizing nature of the optical a/LCI probe means that it can beapplied frequently without adverse affect. The potential of a/LCI toprovide rapid results will greatly enhance its widespread applicabilityfor disease screening.

BRIEF DESCRIPTION OF THE FIGURES

The accompanying drawing figures incorporated in and forming a part ofthis specification illustrate several aspects of the disclosedembodiments, and together with the description serve to explain theprinciples of the disclosed embodiments.

FIG. 1A is a schematic of one exemplary embodiment of the faLCI systememploying Mach-Zehnder interferometer;

FIG. 1B is an illustration showing the relationship of the detectedscattering angle to slit of spectrograph in the interferometerarrangement of FIG. 1A;

FIG. 2 is a flowchart illustrating the steps performed by theinterferometer apparatus to recover depth-resolved spatialcross-correlated information about the sample for analysis;

FIGS. 3A-D illustrate examples of faLCI data recovered in the spectraldomain for an exemplary sample of polystyrene beads, comprising thetotal acquired signal (FIG. 3A), the reference field intensity (FIG.3B), the signal field intensity (FIG. 3C), and the extracted,cross-correlated signal between the reference and signal fieldintensities (FIG. 3D);

FIG. 4A is an illustration of the axial spatial cross-correlatedfunction performed on the cross-correlated faLCI data illustrated inFIG. 3D as a function of depth and angle;

FIG. 4B is an illustration of an angular distribution plot of raw andfiltered data regarding scattered sample signal intensity as a functionof angle in order to recover size information about the sample;

FIG. 5A is an illustration of the filtered angular distribution of thescattered sample signal intensity compared to the best fit Mie theory todetermine size information about the sample;

FIG. 5B is a Chi-squired minimization of size information about thesample to estimate the diameter of cells in the sample;

FIG. 6 is a schematic of exemplary embodiment of the faLCI systememploying an optical fiber probe;

FIG. 7A is a cutaway view of an a/LCI fiber-optic probe tip that may beemployed by the faLCI system illustrated in FIG. 6;

FIG. 7B illustrates the location of the fiber probe in the faLCI systemillustrated in FIG. 7A;

FIG. 8A is an illustration of an alternative fiber-optic faLCI systemthat may be employed with the disclosed embodiments;

FIG. 8B is an illustration of sample illumination and scattered lightcollection with distal end of probe in the faLCI system illustrated inFIG. 8B; and

FIG. 8C is an illustration of an image of the illuminated distal end ofprobe of the faLCI system illustrated in FIG. 8A.

DETAILED DESCRIPTION

The embodiments set forth below represent the necessary information toenable those skilled in the art to practice the disclosed embodimentsand illustrate the best mode of practicing the embodiments. Upon readingthe following description in light of the accompanying drawing figures,those skilled in the art will understand the concepts of the embodimentsand will recognize applications of these concepts not particularlyaddressed herein. It should be understood that these concepts andapplications fall within the scope of the disclosure and theaccompanying claims.

Embodiments disclosed herein involve a new a/LCI technique calledFourier domain a/LCI (faLCI), which enables data acquisition at rapidrates using a single scan, sufficient to make in vivo applicationsfeasible. The embodiments disclosed herein obtain angle-resolved anddepth-resolved spectra information about a sample, in which depth andsize information about the sample can be obtained with a single scan,and wherein the reference arm can remain fixed with respect to thesample due to only one scan required. A reference signal and a reflectedsample signal are cross-correlated and dispersed at a multitude ofreflected angles off of the sample, thereby representing reflectionsfrom a multitude of points on the sample at the same time in parallel.

Since this angle-resolved, cross-correlated signal is spectrallydispersed, the new data acquisition scheme is significant as it permitsdata to be obtained in less than one second, a threshold determined tobe necessary for acquiring data from in vivo tissues. Information aboutall depths of the sample at each of the multitude of different points onthe sample can be obtained with one scan on the order of approximately40 milliseconds. From the spatial, cross-correlated reference signal,structural (size) information can also be obtained using techniques thatallow size information of scatterers to be obtained from angle-resolveddata.

The faLCI technique of the disclosed embodiments uses the Fourier domainconcept to acquire depth resolved information. Signal-to-noise andcommensurate reductions in data acquisition time are possible byrecording the depth scan in the Fourier (or spectral) domain. The faLCIsystem combines the Fourier domain concept with the use of an imagingspectrograph to spectrally record the angular distribution in parallel.Thereafter, the depth-resolution of the disclosed embodiments isachieved by Fourier transforming the spectrum of two mixed fields withthe angle-resolved measurements obtained by locating the entrance slitof the imaging spectrograph in a Fourier transform plane to the sample.This converts the spectral information into depth-resolved informationand the angular information into a transverse spatial distribution. Thecapabilities of faLCI have been initially demonstrated by extracting thesize of polystyrene beads in a depth-resolved measurement.

The key advances of the disclosed embodiments can be broken down intothree components: (1) new rapid data acquisition methods, (2) fiberprobe designs, and (3) data analysis schemes. Thus, the disclosedembodiments are described in this matter for convenience in itsunderstanding.

An exemplary apparatus, as well as the steps involved in the process ofobtaining angle and depth-resolved distribution data scattered from asample, are also set forth in FIG. 2. The faLCI scheme in accordancewith one embodiment of the disclosed embodiments is based on a modifiedMach-Zehnder interferometer as illustrated in FIG. 1A. Broadband light10 from a superluminescent diode (SLD) 12 is directed by a mirror 13(step 60 in FIG. 2) and split into a reference beam 14 and an input beam16 to a sample 18 by beamsplitter BS1 20 (step 62 in FIG. 3). The outputpower of the SLD 12 may be 3 milliWatts, having a specification ofλo=850 nm, Δλ=20 nm FWHM for example, providing sufficiently lowcoherence length to isolate scattering from a cell layer within tissue.The path length of the reference beam 14 is set by adjustingretroreflector RR 22, but remains fixed during measurement. Thereference beam 14 is expanded using lenses L1 (24) and L2 (26) to createillumination (step 64 in FIG. 2), which is uniform and collimated uponreaching a spectrograph slit 48 in an imaging spectrograph 29. Forexample, L1 may have a focal length of 1.5 centimeters, and L2 26 mayhave focal length of 15 centimeters.

Lenses L3 (31) and L4 (38) are arranged to produce a collimated pencilbeam 30 incident on the sample 18 (step 66 in FIG. 2). By displacinglens L4 (38) vertically relative to lens L3 (31), the input beam 30 ismade to strike the sample at an angle of 0.10 radians relative to theoptical axis. This arrangement allows the full angular aperture of lensL4 (38) to be used to collect scattered light 40 from the sample 18.Lens L4 (38) may have a focal length of 3.5 centimeters.

The light 40 scattered by the sample 18 is collected by lens L4 (32) andrelayed by a 4f imaging system comprised of lenses L5 (43) and L6 (44)such that the Fourier plane of lens L4 (32) is reproduced in phase andamplitude at the spectrograph slit 48 (step 68 in FIG. 2). The scatteredlight 40 is mixed with the reference field 14 at a second beamsplitterBS2 42 with the combined fields 46 falling upon the entrance slit(illustrated in FIG. 1B as element 48) to the imaging spectrograph 29(step 70 in FIG. 2). The imaging spectrograph 29 may be the modelSP2150i, manufactured by Acton Research for example. FIG. 1B illustratesthe distribution of scattering angle across the dimension of the slit48. The mixed fields are dispersed with a high resolution grating (e.g.1200 l/mm) and detected using a cooled CCD 50 (e.g. 1340×400, 20 μm×20μm pixels, Spec10:400, manufactured by Princeton Instruments) (step 72in FIG. 2).

The detected signal 46 is a function of vertical position on thespectrograph slit 48, y, and wavelength λ once the light is dispersed bythe spectrograph 29. The detected signal at pixel (m, n) can be relatedto the signal 40 and reference fields 16 (E_(s), E_(r)) as:

I(λ_(m) ,y _(n))=

|E _(r)(λ_(m) ,y _(n))|²

+

|E _(S)(λ_(m) ,y _(n))|²

+2Re

E _(S)(λ_(m) ,y _(n))E _(r)*(λ_(m) ,y _(n))

cos φ,  (1)

where φ is the phase difference between the two fields 30, 16 and

. . .

denotes an ensemble average in time. The interference term is extractedby measuring the intensity of the signal 30 and reference beams 16independently and subtracting them from the total intensity.

In order to obtain depth resolved information, the wavelength spectrumat each scattering angle is interpolated into a wavenumber (k=2π/λ)spectrum and Fourier transformed to give a spatial cross correlation,Γ_(SR)(z) for each vertical pixel y_(n):

Γ_(SR)(z,y _(n))=∫dke ^(ikz)

E _(s)(k,y _(n))E _(r)*(k,y _(n))

cos φ.  (2)

The reference field 14 takes the form:

E _(r)(k)=E _(o)exp└−((k−k _(o))/Δk)²┘exp└−((y−y_(o))/Δy)²┘exp[ikΔl]  (3)

where k_(o) (y_(o) and Δk (Δy) represent the center and width of theGaussian wavevector (spatial) distribution and Δl is the selected pathlength difference. The scattered field 40 takes the form

E _(s)(k,θ)=Σ_(j) E _(o)exp[−((k−k _(o))/Δk)²]exp[ikl _(j) ]S_(j)(k,θ)  (4)

where S_(j) represents the amplitude distribution of the scatteringoriginating from the jth interface, located at depth l_(j). The angulardistribution of the scattered field 40 is converted into a positiondistribution in the Fourier image plane of lens L4 through therelationship y=f₄θ. For the pixel size of the CCD 50 (e.g. 20 μm), thisyields an angular resolution (e.g. 0.57 mrad) and an expected angularrange (e.g. 228 mrad.).

Inserting Eqs. (3) and (4) into Eq. (2) and noting the uniformity of thereference field 14 (Δy>>>slit height) yields the spatial crosscorrelation at the nth vertical position on the detector 29:

$\begin{matrix}{{\Gamma_{SR}\left( {z,y_{n}} \right)} = {\sum\limits_{j}{\int{{k}{E_{o}}^{2}{\exp \left\lbrack {{- 2}\left( {\left( {k - k_{o}} \right)\Delta \; k} \right)^{2}} \right\rbrack}{\exp \left\lbrack {\; {k\left( {z - {\Delta \; l} + l_{j}} \right)}} \right\rbrack} \times {S_{j}\left( {k,{\theta_{n} = {y_{n}/f_{4}}}} \right)}\cos \; {\varphi.}}}}} & (5)\end{matrix}$

Evaluating this equation for a single interface yields:

Γ_(SR)(z,y _(n))=|E _(o)|²exp[−((z−Δl+l _(j))Δk)²/8]S _(j)(k _(o),θ_(n)=y _(n) /f ₄)cos φ.  (6)

Here we have assumed that the scattering amplitude S does not varyappreciably over the bandwidth of the source light 12. This expressionshows that we obtain a depth resolved profile of the scatteringdistribution 40 with each vertical pixel corresponding to a scatteringangle.

FIG. 3A below shows typical data representing the total detectedintensity (Equation (1), above) of the sum of the reference field 16 andthe field scattered 40 by a sample of polystyrene beads, in thefrequency domain given as a function of wavelength and angle, given withrespect to the backwards scattering direction. In an exemplaryembodiment, this data was acquired in 40 milliseconds and records dataover 186 mrad, approximately 85% of the expected range, with some lossof signal at higher angles.

FIGS. 3B and 3C illustrate the intensity of the reference and signalfields 14, respectively. Upon subtraction of the signal and referencefields 14, 30 from the total detected intensity, the interference 46between the two fields is realized as illustrated in FIG. 3D. At eachangle, interference data 46 are interpolated into k-space and Fouriertransformed to give the angular depth resolved profiles of the sample 18as illustrated in FIG. 4A. The Fourier transform of the angle-resolved,cross correlated signal 46, which is the result of signal 40 scatteredat a multitude of reflected angles off the sample 18 and obtained in theFourier plane of lens L4 (38), produces depth-resolved information aboutthe sample 18 as a function of angle and depth. This providesdepth-resolved information about the sample 18. Because theangle-resolved, cross-correlated signal 46 is spectrally dispersed, thedata acquisition permits data to be obtained in less than one second.Information about all depths of the sample 18 at each of the multitudeof different points (i.e. angles) on the sample 18 can be obtained withone scan on the order of approximately 40 milliseconds. Normally, timedomain based scanning is required to obtain information about all depthsof a sample at a multitude of different points, thus requiringsubstantial time and movement of the reference arm with respect to thesample.

In the experiments that produced the depth-resolved profile of thesample 18 illustrated in FIG. 4A, the sample 18 consists of polystyrenemicrospheres (e.g. n=1.59, 10.1 μm mean diameter, 8.9% variance, NISTcertified, Duke Scientific) suspended in a mixture of 80% water and 20%glycerol (n=1.36) to provide neutral buoyancy. The solution was preparedto obtain a scattering length l=200 μm. The sample is contained in around well (8 mm diameter, 1 mm deep) behind a glass coverslip(thickness, d˜170 μm) (not shown). The sample beam 30 is incident on thesample 18 through the coverslip. The round trip thickness through thecoverslip (2 n d=2 (1.5) (170 μm)=0.53 mm—see FIG. 4A) shows the depthresolved capability of the approach. The data are ensemble averaged byintegrating over one mean free path (MFP). The spatial average canenable a reduction of speckle when using low-coherence light to probe ascattering sample. To simplify the fitting procedure, the scatteringdistribution is low pass filtered to produce a smoother curve, with thecutoff frequency chosen to suppress spatial correlations on lengthscales above 16 μm.

In addition to obtaining depth-resolved information about the sample 18,the scattering distribution data (i.e. a/LCI data) obtained from thesample 18 using the disclosed data acquisition scheme can also be usedto make a size determination of the nucleus using the Mie theory. Ascattering distribution 74 of the sample 18 is illustrated in FIG. 4B asa contour plot. The raw scattered information 74 about the sample 18 isshown as a function of the signal field 30 and angle. A filtered curveis determined using the scattered data 74. Comparison of the filteredscattering distribution curve 76 (i.e. a representation of the scattereddata 74) to the prediction of Mie theory (curve 78 in FIG. 5A) enables asize determination to be made.

In order to fit the scattered data 76 to Mie theory, the a/LCI signalsare processed to extract the oscillatory component which ischaracteristic of the nucleus size. The smoothed data 76 are fit to alow-order polynomial (4^(th) order was used for example herein, butlater studies use a lower 2^(nd) order), which is then subtracted fromthe distribution 76 to remove the background trend. The resultingoscillatory component is then compared to a database of theoreticalpredictions obtained using Mie theory 78 from which the slowly varyingfeatures were similarly removed for analysis.

A direct comparison between the filtered a/LCI data 76 and Mie theorydata 78 may not possible, as the chi-squared fitting algorithm tends tomatch the background slope rather than the characteristic oscillations.The calculated theoretical predictions include a Gaussian distributionof sizes characterized by a mean diameter (d) and standard deviation(ED) as well as a distribution of wavelengths, to accurately model thebroad bandwidth source.

The best fit (FIG. 5A) is determined by minimizing the Chi-squaredbetween the data 76 and Mie theory (FIG. 5B), yielding a size of10.2+/−1.7 μm, in excellent agreement with the true size. Themeasurement error is larger than the variance of the bead size, mostlikely due to the limited range of angles recorded in the measurement.

As an alternative to processing the a/LCI data and comparing to Mietheory, there are several other approaches which could yield diagnosticinformation. These include analyzing the angular data using a Fouriertransform to identify periodic oscillations characteristic of cellnuclei. The periodic oscillations can be correlated with nuclear sizeand thus will possess diagnostic value. Another approach to analyzinga/LCI data is to compare the data to a database of angular scatteringdistributions generated with finite element method (FEM) or T-Matrixcalculations. Such calculations may offer superior analysis as there arenot subject to the same limitations as Mie theory. For example, FEM orT-Matrix calculations can model non-spherical scatterers and scattererswith inclusions while Mie theory can only model homogenous spheres.

As an alternative embodiment, the disclosed embodiments can also employoptical fibers to deliver and collect light from the sample of interestto use in the a/LCI system for endoscopic applications. This alternativeembodiment is illustrated in FIG. 6.

The fiber optic a/LCI scheme for this alternative embodiment makes useof the Fourier transform properties of a lens. This property states thatwhen an object is placed in the front focal plane of a lens, the imageat the conjugate image plane is the Fourier transform of that object.The Fourier transform of a spatial distribution (object or image) isgiven by the distribution of spatial frequencies, which is therepresentation of the image's information content in terms of cycles permm. In an optical image of elastically scattered light, the wavelengthretains its fixed, original value and the spatial frequencyrepresentation is simply a scaled version of the angular distribution ofscattered light.

In the fiber optic a/LCI scheme, the angular distribution is captured bylocating the distal end of the fiber bundle in a conjugate Fouriertransform plane of the sample using a collecting lens. This angulardistribution is then conveyed to the distal end of the fiber bundlewhere it is imaged using a 4f system onto the entrance slit of animaging spectrograph. A beamsplitter is used to overlap the scatteredfield with a reference field prior to entering the slit so that lowcoherence interferometry can also be used to obtain depth resolvedmeasurements.

Turning now to FIG. 6, the fiber optic faLCI scheme is shown. Light 12′from a broadband light source 10′ is split into a reference field 14′and a signal field 16′ using a fiber splitter (FS) 80. A splitter ratioof 20:1 is chosen in one embodiment to direct more power to a sample 18′via the signal arm 82 as the light returned by the tissue is typicallyonly a small fraction of the incident power.

Light in the reference fiber 14′ emerges from fiber F1 and is collimatedby lens L1 (84) which is mounted on a translation stage 86 to allowgross alignment of the reference arm path length. This path length isnot scanned during operation but may be varied during alignment. Acollimated beam 88 is arranged to be equal in dimension to the end 91 offiber bundle F3 (90) so that the collimated beam 88 illuminates allfibers in F3 with equal intensity. The reference field 14′ emerging fromthe distal tip of F3 (90) is collimated with lens L3 (92) in order tooverlap with the scattered field conveyed by fiber F4 (94). In analternative embodiment, light emerging from fiber F1 (14′) is collimatedthen expanded using a lens system to produce a broad beam.

The scattered field is detected using a coherent fiber bundle. Thescattered field is generated using light in the signal arm 82 which isdirected toward the sample 18′ of interest using lens L2 (98). As withthe free space system, lens L2 (98) is displaced laterally from thecenter of single-mode fiber F2 such that a collimated beam is producedwhich is traveling at an angle relative to the optical axis The factthat the incident beam strikes the sample at an oblique angle isessential in separating the elastic scattering information from specularreflections. The light scattered by the sample 18′ is collected by afiber bundle consisting of an array of coherent single mode ormulti-mode fibers. The distal tip of the fiber is maintained one focallength away from lens L2 (98) to image the angular distribution ofscattered light. In the embodiment shown in FIG. 6, the sample 18′ islocated in the front focal plane of lens L2 (98) using a mechanicalmount 100. In the endoscope compatible probe shown in FIG. 7, the sampleis located in the front focal plane of lens L2 (98) using a transparentsheath (element 102).

As illustrated in FIG. 6 and also FIG. 7B, scattered light 104 emergingfrom a proximal end 105 of the fiber probe F4 (94) is recollimated bylens L4 (104) and overlapped with the reference field 14′ usingbeamsplitter BS (108). The two combined fields 110 are re-imaged ontothe slit (element 48′ in FIG. 7) of the imaging spectrograph 29′ usinglens L5 (112). The focal length of lens L5 (112) may be varied tooptimally fill the slit 48′. The resulting optical signal containsinformation on each scattering angle across the vertical dimension ofthe slit 48′ as described above for the apparatus of FIGS. 1A and 1B.

It is expected that the above-described a/LCI fiber-optic probe willcollect the angular distribution over a 0.45 radian range (approx. 30degrees) and will acquire the complete depth resolved scatteringdistribution 110 in a fraction of a second.

There are several possible schemes for creating the fiber probe whichare the same from an optical engineering point of view. One possibleimplementation would be a linear array of single mode fibers in both thesignal and reference arms. Alternatively, the reference arm 96 could becomposed of an individual single mode fiber with the signal arm 82consisting of either a coherent fiber bundle or linear fiber array.

The fiber probe tip can also have several implementations which aresubstantially equivalent. These would include the use of a drum or balllens in place of lens L2 (98). A side-viewing probe could be createdusing a combination of a lens and a minor or prism or through the use ofa convex minor to replace the lens-minor combination. Finally, theentire probe can be made to rotate radially in order to provide acircumferential scan of the probed area.

Yet another data acquisition embodiment of the disclosed embodimentscould be a fa/LCI system is based on a modified Mach-Zehnderinterferometer as illustrated in FIG. 5A. The output 10″ from afiber-coupled superluminescent diode (SLD) source 12″ (e.g. Superlum,P_(o)=15 mW, λo=841.5 nm, Δλ=49.5 nm, coherence length=6.3 μm) is splitinto sample arm delivery fiber 16″ and a reference arm delivery fiber14″ by a 90/10 fiber splitter FS (80′) (e.g. manufactured by ACPhotonics). The sample arm delivery fiber 16″ can consist of either ofthe following for example: (1) a single mode fiber with polarizationcontrol integrated at the tip; or (2) a polarization maintaining fiber.A sample probe 113 is assembled by affixing the delivery fiber16″(NA≅0.12) along the ferrule 114 at the distal end of a fiber bundle116 such that the end face of the delivery fiber 16″ is parallel to andflush with the face of the fiber bundle 116. Ball lens L1 (115) (e.g.f=2.2 mm) is positioned one focal length from the face of the probe 113and centered on the fiber bundle 116, offsetting the delivery fiber 16″from the optical axis of lens L1 (115). This configuration, which isalso depicted in FIG. 8B, produces a collimated beam 120 (e.g. P=9 mW)with a diameter (e.g. 2f₁NA) of 0.5 mm incident on the sample 18″ at anangle of 0.25 rad. for example.

The scattered light 122 from the sample is collected by lens L1 (115)and, via the Fourier transform property of the lens L1 (115, the angulardistribution of the scattered field 122 is converted into a spatialdistribution at the distal face of the multimode coherent fiber bundle116 (e.g. Schott North America, Inc., length=840 mm, pixel size=8.2 μm,pixel count=13.5K) which is located at the Fourier image plane of lensL1 (115). The relationship between vertical position on the fiberbundle, y′, and scattering angle, θ is given by y′=f₁θ. As anillustration, the optical path of light scattered 122 at three selectedscattering angles is shown in FIG. 8B. Overall, the angular distributionis sampled by approximately 130 individual fibers for example, across avertical strip of the fiber bundle 116″, as depicted by the highlightedarea in FIG. 8C. The 0.2 mm, for example, thick ferrule (d₁) separatingthe delivery fiber 16″ and fiber bundle 116 limits the minimumtheoretical collection angle (θ_(min,th)=d₁/f₁) to 0.09 rad in thisexample. The maximum theoretical collection angle is determined by d₁and d₂, the diameter of the fiber bundle, by θ_(max,th)=(d₁+d₂)/f₁ to be0.50 rad. Experiments using a standard scattering sample 122 indicatethe usable angular range to be θ_(min)=0.12 rad. to θ_(max)=0.45 rad.d₁, for example, can be minimized by fabricating a channel in the distalferrule 123 and positioning the delivery fiber 16″ in the channel. Thefiber bundle 116 is spatially coherent, resulting in a reproduction ofthe collected angular scattering distribution at the proximal face.Additionally, as all fibers in the bundle 116 are path length matched towithin the coherence length, the optical path length traveled byscattered light 122 at each angle is identical. The system disclosed in“Fiber-optic-bundle-based optical coherence tomography,” by T. Q. Xie,D. Mukai, S. G. Guo, M. Brenner, and Z. P. Chen in Optics Letters30(14), 1803-1805 (2005) (hereinafter “Xie”), incorporated by referenceherein in its entirety, discloses a multimode coherent fiber bundle intoa time-domain optical coherence tomography system and demonstrated thatthe modes of light coupled into an individual fiber will traveldifferent path lengths. In the example herein of the disclosedembodiments, it was experimentally determined that the higher ordermodes are offset from the fundamental mode by 3.75 mm, well beyond thedepth (˜100 μm) required for gathering clinically relevant data.Additionally, the power in the higher order modes had a minimal affecton dynamic range as the sample arm power is significantly less than thereference arm power. Finally, it should be noted that while the systemdisclosed in Xie collected data serially through individual fibers, theexample of the disclosed embodiments herein uses 130 fibers tosimultaneously collect scattered light across a range of angles inparallel, resulting in rapid data collection.

The angular distribution exiting a proximal end 124 of the fiber bundle116 is relayed by the 4f imaging system of L2 and L3 (f₂=3.0 cm, f₃=20.0cm) to the input slit 48″ of the imaging spectrograph 29″ (e.g. ActonResearch, InSpectrum 150). The theoretical magnification of the 4fimaging system is (f₃/f₂) 6.67 in this example. Experimentally, themagnification was measured to be M=7.0 in this example with thediscrepancy most likely due to the position of the proximal face 124 ofthe fiber bundle 116 with relation to lens L2 (126). The resultingrelationship between vertical position on the spectrograph slit 48″, y,and θ is y=Mf₁ (θ−θ_(min)). The optical path length of the reference armis matched to that of the fundamental mode of the sample arm. Light 127exiting the reference fiber 14″ is collimated by lens L4 (128) (e.g.f=3.5 cm, spot size=8.4 mm) to match the phase front curvature of thesample light and to produce even illumination across the slit 48″ of theimaging spectrograph 29″. A reference field 130 may be attenuated by aneutral density filter 132 and mixed with the angular scatteringdistribution at beamsplitter BS (134). The mixed fields 136 aredispersed with a high resolution grating (e.g. 1200 lines/mm) anddetected using an integrated, cooled CCD (not shown) (e.g. 1024×252, 24μm×24 μm pixels, 0.1 nm resolution) covering a spectral range of 99 nmcentered at 840 nm, for example.

The detected signal 136, a function of wavelength, 2, and 0, can berelated to the signal and reference fields (Es, Er) as:

I(λ_(m) ,y _(n))=

|E _(r)(λ_(m) ,y _(n))|²

+

|E _(S)(λ_(m) ,y _(n))|²

+2Re

E _(S)(λ_(m) ,y _(n))E _(r)*(λ_(m) ,y _(n))

cos φ,  (1)

where φ is the phase difference between the two fields, (m,n) denotes apixel on the CCD, and

. . .

denotes a temporal average. I(λ_(m),θ_(n)) is uploaded to a PC usingLabVIEW manufactured by National Instruments software and processed in320 ms to produce a depth and angle resolved contour plot of scatteredintensity. The processing of the angle-resolved scattered field toobtain depth and size information described above, and in particularreference to the data acquisition apparatus of FIGS. 1A and 1B, can thenused to obtain angle-resolved, depth-resolved information about thesample 18″ using the scattered mixed field 136 generated by theapparatus in FIG. 8.

The embodiments set forth above represent the necessary information toenable those skilled in the art to practice the disclosed embodimentsand illustrate the best mode of practicing the disclosed embodiments.Upon reading the following description in light if the accompanyingdrawings figures, those skilled in the art will understand the conceptsof the disclosed embodiments and will recognize applications of theseconcepts not particularly addressed herein. It should be understood thatthese concepts and applications fall within the scope of the disclosure.

Those skilled in the art will recognize improvements and modificationsto the preferred embodiments of the disclosed embodiments. All suchimprovements and modifications are considered within the scope of theconcepts disclosed herein and the claims that follow.

1. A method of obtaining depth-resolved spectra of a sample fordetermining characteristics within the sample, comprising: emitting asource beam onto a splitter, wherein the splitter splits light from thesource beam to produce a reference beam and a sample beam; directing thesample beam towards the sample at an angle while maintaining an opticalpath length of the sample beam to the sample; receiving anangle-resolved scattered sample beam as a result of the sample beamscattering at a multitude of scattered angles off of the sample, whereinthe angle-resolved scattered sample beam contains the angular scatteringdistribution of the scattered sample beam; cross-correlating theangle-resolved scattered sample beam with the reference beam to producean angle-resolved cross-correlated signal about the sample; spectrallydispersing the angle-resolved cross-correlated signal to yield anangle-resolved, spectrally-resolved cross-correlation profile havingdepth-resolved information about the sample at the multitude ofscattered angles; and processing the angle-resolved, spectrally-resolvedcross-correlation profile to obtain depth-resolved information about thesample.
 2. The method of claim 1, further comprising determining thedepth of the scatterers of the sample at a multitude of different pointson the sample from the angle-resolved, spectrally-resolvedcross-correlation profile.
 3. The method of claim 1, wherein processingthe angle-resolved, spectrally-resolved cross-correlation profilecomprises Fourier transforming the angle-resolved, spectrally-resolvedcross-correlation profile to produce depth-resolved information aboutthe sample.
 4. The method of claim 1, further comprising recovering sizeinformation about the scatterers from the angle-resolved,spectrally-resolved cross-correlation profile.
 5. The method of claim 4,wherein recovering the size information comprises comparing the angularscattering distribution of the angle-resolved, spectrally-resolvedcross-correlation profile to a database of angular scatteringdistributions generated with a finite element method (FEM) or T-Matrixcalculations.
 6. The method of claim 4, wherein recovering the sizeinformation comprises comparing the angular scattering distribution ofthe angle-resolved, spectrally-resolved cross-correlation profile to apredicted analytically or numerically calculated angular scatteringdistribution of the sample.
 7. The method of claim 6, wherein thepredicted analytically or numerically calculated angular scatteringdistribution of the sample is a Mie theory angular scatteringdistribution of the sample.
 8. The method of claim 6, further comprisingfiltering the angular scattering distribution of the sample beforecomparing the angular scattering distribution.
 9. The method of claim 6,further comprising calculating a Gaussian distribution of sizes of thescatterers by calculating a mean diameter and a standard deviation tomodel the angular scattering distribution of the sample.
 10. The methodof claim 1, further comprising collimating the sample beam to produce acollimated sample beam, wherein directing the sample beam towards thesample at an angle comprises directing the collimated sample beamtowards the sample at an angle.
 11. The method of claim 1, furthercomprising collimating the reference beam to produce a collimatedreference beam.
 12. The method of claim 1, wherein the reference beam isreflected before the cross-correlating to create a reflected referencebeam.
 13. The method of claim 12, wherein the reflected reference beamis created by reflecting the reference beam off of a reference minor.14. The method of claim 1, wherein cross-correlating the angle-resolvedscattered sample beam with the reference beam comprises: determining aninterference term by measuring the intensity of the angle-resolvedscattered sample beam and the reference beam independently; andsubtracting the interference term from the total intensity of theangle-resolved scattered sample beam.
 15. The method of claim 1, furthercomprising maintaining an optical path length of the reference beam. 16.The method of claim 1, wherein spectrally dispersing the angle-resolvedcross-correlated signal comprises directing the angle-resolved scatteredsample beam which has been combined with the reference beam into aspectrograph.
 17. The method of claim 16, wherein the spectrographcomprises an imaging spectrograph comprised of a plurality of imagingpoints wherein each of the plurality of imaging points corresponds to aspecific scattering angle in order to produce the angle-resolved,spectrally-resolved cross-correlation profile about the sample.
 18. Themethod of claim 16, wherein the spectrograph comprises a multi-channelspectrograph comprised of a plurality of channels, wherein each of theplurality of channels corresponds to a specific scattering angle inorder to produce the angle-resolved, spectrally-resolvedcross-correlation profile about the sample.
 19. The method of claim 1,wherein receiving the angle-resolved scattered sample beam as a resultof the sample beam scattering at the multitude of scattered angles offof the sample in parallel comprises capturing the angular distributionof the scattered sample beam at an end of a fiber bundle comprised of aplurality of fibers.
 20. The method of claim 19, wherein the pluralityof fibers in the fiber bundle are arranged to collect different angularscatterings of the scattered sample beam to collect the angularscattering distribution of the scattered sample beam.
 21. The method ofclaim 19, wherein the fiber bundle comprises a linear array of singlemode fibers.
 22. The method of claim 19, further comprising carrying thesample beam on a delivery fiber wherein the delivery fiber delivers thesample beam at an oblique angle with respect to the sample and the fiberbundle so that a specular reflection due to the sample is not receivedby the fiber bundle.
 23. The method of claim 19, further comprisingreceiving the angle-resolved scattered sample beam via a Fouriertransform property of an optical element placed in between the fiberbundle and the sample to receive the angle-resolved scattered samplebeam located at another focus of the optical element.
 24. The method ofclaim 19, wherein the plurality of fibers possess the same orsubstantially the same spatial arrangement at distal and proximal endsof the plurality of fibers so that the fiber bundle is spatiallycoherent with respect to conveying the angular distribution of theangle-resolved scattered sample beam.
 25. The method of claim 23,wherein the optical element is either a lens or an imaging opticalelement.
 26. The method of claim 1, further comprising splitting morelight at the splitter from the source beam to produce more light in thesample beam than in the reference beam.
 27. The method of claim 1,further comprising varying an optical path length of the reference beamto align the optical path length of the reference beam to the opticalpath length of the sample beam.
 28. An apparatus for obtainingdepth-resolved spectra of a sample for determining characteristicswithin the sample, comprising: a receiver configured to: receive anangle-resolved scattered sample beam as a result of a sample beam, splitby a splitter from a source beam, scattered at a multitude of scatteredangles off of the sample, wherein the angle-resolved scattered samplebeam contains the angular scattering distribution of the scatteredsample beam while maintaining an optical path length of the sample beamto the sample; receive a reference beam split by the splitter from thesource beam; and cross-correlate the angle-resolved scattered samplebeam with the reference beam to produce an angle-resolvedcross-correlated signal about the sample; a detector configured tospectrally disperse the angle-resolved cross-correlated signal to yieldan angle-resolved, spectrally-resolved cross-correlation profile havingdepth-resolved information about the sample at the multitude ofscattered angles; and a processor configured to receive theangle-resolved, spectrally-resolved cross-correlation profile.
 29. Theapparatus of claim 28, wherein the processor is configured to determinethe depth of the scatterers of the sample at a multitude of differentpoints on the sample from the angle-resolved, spectrally-resolvedcross-correlation profile.
 30. The apparatus of claim 28, wherein theprocessor is further configured to Fourier transform the angle-resolved,spectrally-resolved cross-correlation profile to produce depth-resolvedinformation about the sample as a function of angle and depth.
 31. Theapparatus of claim 28, wherein the processor is further configured torecover size information about the scatterers from the angle-resolved,spectrally-resolved cross-correlation profile.
 32. The apparatus ofclaim 31, wherein the processor recovers the size information bycomparing the angular scattering distribution of the sample to apredicted analytically or numerically calculated angular scatteringdistribution of the sample.
 33. The apparatus of claim 32, wherein thepredicted analytically or numerically calculated angular scatteringdistribution of the sample is a Mie theory angular scatteringdistribution of the sample.
 34. The apparatus of claim 32, wherein theprocessor is further configured to filter the angular scatteringdistribution of the sample before comparing the angular scatteringdistribution of the sample to a predicted analytically or numericallycalculated angular scattering distribution of the sample.
 35. Theapparatus of claim 34, wherein the processor is further configured toidentify a Gaussian distribution of sizes of the scatterers byidentifying a mean diameter and a standard deviation to model theangular scattering distribution.
 36. The apparatus of claim 28, whereinthe sample beam is collimated.
 37. The apparatus of claim 28, whereinthe reference beam is collimated.
 38. The apparatus of claim 28, furthercomprising a reflection device configured to receive and reflect thereference beam wherein the receiver receives the reflected referencebeam.
 39. The apparatus of claim 38, wherein the reflection device is areference mirror.
 40. The apparatus of claim 28, wherein the splitter isan optical fiber splitter.
 41. The apparatus of claim 28, wherein thesource beam is comprised of a light selected from the group consistingof a white light from an arc lamp, a thermal source, a light-emittingdiode (LED), a coherent light from a broadband laser, a superluminescentdiode, a diode laser, and a supercontinuum source.
 42. The apparatus ofclaim 28, wherein the splitter is attached to a reference arm.
 43. Theapparatus of claim 28, wherein the sample is attached to a sample arm.44. The apparatus of claim 28, wherein the detector comprises aspectrograph.
 45. The apparatus of claim 28, wherein the receiver is afiber bundle comprised of a plurality of fibers.
 46. The apparatus ofclaim 45, wherein the plurality of fibers in the fiber bundle arearranged to collect different angular scatterings of the scatteredsample beam to collect the angular scattering distribution of theangle-resolved scattered sample beam.
 47. The apparatus of claim 46,wherein the fiber bundle comprises a linear array of single mode fibers.48. The apparatus of claim 46, further comprising a delivery fiber thatcarries the sample beam so that the delivery fiber delivers the samplebeam at an oblique angle with respect to the sample and the fiber bundleso that a specular reflection due to the sample is not received by thefiber bundle.
 49. The apparatus of claim 46, wherein the plurality offibers is positioned at one focus of an optical element to receive theangle-resolved scattered sample beam which is located at another focusof the optical element such that the fiber bundle receives the angularscattering distribution of scattered light via a Fourier transformproperty of the optical element.
 50. The apparatus of claim 49, whereinthe optical element is either a lens or an imaging optical element. 51.The apparatus of claim 46, wherein the plurality of fibers possess thesame or substantially the same spatial arrangement at distal andproximal ends of the plurality of fibers so that the fiber bundle isspatially coherent with respect to conveying the angular scatteringdistribution of the angle-resolved scattered sample beam.
 52. Theapparatus of claim 28, wherein the splitter splits more light from thesource beam to produce the sample beam than to produce the referencebeam.
 53. An apparatus for obtaining depth-resolved spectra of a samplefor determining characteristics within the sample, comprising: at leastone delivery fiber that carries a sample beam wherein the sample beam isdirected to the sample over the at least one delivery fiber whilemaintaining an optical path length of the sample beam to the sample andscattered at a multitude of angles off of the sample to produce ascattered sample beam; a fiber-optic receiver comprised of a pluralityof fibers configured to receive the scattered sample beam from thesample, such that the fiber-optic receiver receives an angularscattering distribution of the scattered sample beam; a beam splitterconfigured to cross-correlate the angular scattering distribution of thescattered sample beam with a reference beam to produce an angle-resolvedcross-correlated signal about the sample; a detector that spectrallydisperses the angle-resolved cross-correlated signal to yield anangle-resolved, spectrally-resolved cross-correlation profile at each ofthe multitude of angles; and a processor configured to receive andanalyze the angle-resolved, spectrally-resolved cross-correlationprofile.
 54. The apparatus of claim 53, wherein the processor is furtherconfigured to obtain depth-resolved information about the sample fromthe angle-resolved, spectrally-resolved cross-correlation profile. 55.The apparatus of claim 53, wherein the processor is further configuredto process the angle-resolved cross-correlated signal to obtaindepth-resolved information about the scatterers of the sample at amultitude of different points on the sample from the angle-resolved,spectrally-resolved cross-correlation profile.
 56. The apparatus ofclaim 53, wherein the processor is further configured to recover sizeinformation about the scatterers from the angle-resolved,spectrally-resolved cross-correlation profile.
 57. The apparatus ofclaim 53, wherein the plurality of fibers in the fiber-optic receiverare arranged to collect different angular scatterings of the sample beamto collect the angular scattering distribution of the scattered samplebeam.
 58. The apparatus of claim 53, wherein the fiber-optic receivercomprises a linear array of single mode fibers.
 59. The apparatus ofclaim 53, wherein the plurality of fibers possess the same spatialarrangement at distal and proximal ends of the plurality of fibers sothat the fiber-optic receiver is spatially coherent with respect toconveying the angular scattering distribution of the scattered samplebeam.
 60. The apparatus of claim 53, wherein the plurality of fibers ispositioned at one focus of an optical element to receive the scatteredsample beam which is located at another focus of the optical elementsuch that the fiber-optic receiver receives the angular scatteringdistribution of scattered light.
 61. The apparatus of claim 60, whereinthe fiber-optic receiver receives the angular scattering distribution ofscattered light via a Fourier transform property of the optical element.62. The apparatus of claim 60, wherein the optical element is either alens or an imaging optical element.
 63. The apparatus of claim 53,wherein the processor is further configured to Fourier transform theangled-resolved, spectrally-resolved cross-correlation profile toproduce depth-resolved information about the sample as a function ofangle and depth.
 64. The apparatus of claim 53, wherein a distal end ofthe fiber-optic receiver is located in a conjugate Fourier transformplane of the sample.
 65. The apparatus of claim 53, wherein thereference beam is collimated to overlap with the scattered sample beamfrom the sample.
 66. The apparatus of claim 53, wherein the fiber-opticreceiver is comprised of a fiber-optic bundle.